Combined characterization and inversion of reservoir parameters from nuclear, NMR and resistivity measurements

ABSTRACT

The present invention is method of determining the distribution of shales, sands and water in a reservoir including laminated shaly sands using vertical and horizontal conductivities derived from nuclear, NMR, and multi-component induction data such as from a Transverse Induction Logging Tool (TILT). Making assumptions about the anisotropic properties of the laminated shale component and an assumption that the sand is isotropic, the TILT data are inverted. An estimate of the laminated shale volume from this inversion is compared with an estimate of laminated shale volume from nuclear logs using a Thomas-Stieber and Waxman-Smits model. A difference between the two estimates is an indication that the sands may be anisotropic. A check is made to see if a bulk water volume determined from the inversion is greater than a bulk irreducible water volume from NMR measurements. In one embodiment of the invention, NMR data are then used to obtain sand distribution in the reservoir. This sand distribution is used in a second inversion of the TILT data, assuming that the sand comprises a number of intrinsically isotropic layers, to give a model that comprises laminated sands including water and dispersed clay, laminated shales and clay-bound water. In another embodiment of the invention, a bulk permeability measurement is used as a constraint in inverting the properties of the anisotropic sand component of the reservoir. From the resistivities of the sand laminae, empirical relations are used to predict anisotropic reservoir properties of the reservoir.

CROSS REFERENCES TO RELATED APPLICATIONS

[0001] This application claims priority from U.S. Provisional patentapplication Ser. No. 60/229,134 filed on Aug. 30, 2000.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The invention is related generally to the field of interpretationof measurements made by well logging instruments for the purpose ofdetermining the fluid content and permeability of earth formations. Morespecifically, the invention is related to methods for using Nuclear,Resistivity and Nuclear Magnetic Resonance (NMR) measurements and/ormeasurements made with a formation testing tool or pressure tests madein laminated reservoirs for determining a distribution of sands, shalesand fluids in the reservoir and estimating permeability of thereservoir.

[0004] 2. Background of the Art

[0005] A significant number of hydrocarbon reservoirs include deep waterturbidite deposits that consist of thin bedded, laminated sands andshales. A common method for evaluating the hydrocarbon content ofreservoirs is the use of resistivity measurements. In interpretationtechniques known in the art, typically one or more types ofporosity-related measurement will be combined with measurements of theelectrical resistivity (or its inverse, electrical conductivity) of theearth formations to infer the fluid content within the pore spaces ofthe earth formations. The fractional volumes of connate water andhydrocarbons can be inferred from empirical relationships of formationresistivity Rt with respect to porosity and connate water resistivitysuch as, for example, the well known Archie relationship. In the Archierelationship fractional volume of water in the pore space isrepresented, as shown in the following expression, by Sw—known as “watersaturation”: $\begin{matrix}{S_{w}^{n} = {\frac{R_{0}}{R_{t}} = {\frac{1}{R_{t}}\frac{{aR}_{w}}{\varphi^{m}}}}} & (1)\end{matrix}$

[0006] where a and m are empirically determined factors which relate theporosity (represented by Φ) to the resistivity of the porous rockformation when it is completely water-saturated (R₀), R_(w) representsthe resistivity of the connate water disposed in the pore spaces of theformation, and m represents an empirically determined “cementation”exponent, n is the saturation exponent.

[0007] Relationships such as the Archie formula shown in equation (1) donot work very well when the particular earth formation being analyzedincludes some amount of extremely fine-grained, clay mineral-basedcomponents known in the art as “shale”. Shale typically occurs, amongother ways, in earth formations as “dispersed” shale, where particles ofclay minerals occupy some of the pore spaces in the hydrocarbon-bearingearth formations, or as laminations (layers) of clay mineral-based rockinterleaved with layers of reservoir-type rock in a particular earthformation.

[0008] In the case of dispersed shale, various empirically derivedrelationships have been developed to calculate the fractional volume ofpore space which is capable of containing movable (producible)hydrocarbons. The fractional volume of such formations which is occupiedby dispersed shale can be estimated using such well logging devices asnatural gamma ray radiation detectors. See for example, M. H. Waxman etal, “Electrical Conductivities in Oil Bearing Shaly Sands”, SPE Journal,vol. 8, no. 2, Society of Petroleum Engineers, Richardson, Tex. (1968).

[0009] In the case of laminated shale, the layers sometimes are thickenough to be within the vertical resolution of, and therefore aredeterminable by, well logging instruments such as a natural gamma raydetector. In these cases, the shale layers are determined not to bereservoir rock formation and are generally ignored for purposes ofdetermining hydrocarbon content of the particular earth formation. Aproblem in laminated shale reservoirs is where the shale laminations arenot thick enough to be fully determined using gamma ray detectors andare not thick enough to have their electrical resistivity accuratelydetermined by electrical resistivity measuring devices known in the art.

[0010] Sands that have high hydrocarbon saturation are typically moreresistive than shales. In reservoirs consisting of thin laminations ofsands and shales, conventional induction logging tools greatlyunderestimate the resistivity of the reservoir: the currents induced inthe formation by the logging tool flow preferentially through theconductive shale laminations creating a bias towards a higher formationconductivity. This could lead to an underestimation of hydrocarbonreserves.

[0011] One method for estimating hydrocarbon content of earth formationswhere shale laminations are present was developed by Poupon. See A.Poupon et al, “A Contribution to Electrical Log Interpretation in ShalySands”, Transactions AIME, Vol. 201, pp. 138-145 (1959). Generally thePoupon relationship assumes that the shale layers affect the overallelectrical conductivity of the earth formation being analyzed inproportion to the fractional volume of the shale layers within theparticular earth formation being analyzed. The fractional volume istypically represented by V_(sh) (shale “volume”). Poupon's model alsoassumes that the electrical conductivity measured by the well logginginstrument will include proportional effects of the shale layers,leaving the remainder of the measured electrical conductivity asoriginating in the “clean” (non-shale bearing) reservoir rock layers asshown in the following expression: $\begin{matrix}{\frac{1}{R_{t}} = {{\left( {1 - V_{sh}} \right)\left( \frac{{aR}_{w}}{\varphi^{m}} \right)^{- 1}S_{w}^{n}} + \frac{V_{sh}}{R_{sh}}}} & (2)\end{matrix}$

[0012] where R_(t) represents the electrical resistivity (inverse ofconductivity) in the reservoir rock layers of the formation and R_(sh)represents the resistivity in the shale layers.

[0013] The analysis by Poupon overlooks the effect of anisotropy in theresistivity of a reservoir including thinly laminated sands and shales.Use of improper evaluation models in many cases may result in anunderestimation of reservoir producibility and hydrocarbon reserves by40% or more as noted by van den Berg and Sandor. Analysis of welllogging instrument measurements for determining the fluid content ofpossible hydrocarbon reservoirs includes calculating the fractionalvolume of pore space (“porosity”) and calculating the fractional volumeswithin the pore spaces of both hydrocarbons and connate water. As notedabove, Archie's relationship may be used.

[0014] In thinly laminated reservoirs where the wavelength of theinterrogating electromagnetic wave is greater than the thickness of theindividual layers, the reservoir exhibits an anisotropy in theresistivity. This anisotropy may be detected by using a logging toolthat has, in addition to the usual transmitter coil and receiver coilaligned along with the axis of the borehole, a receiver or a transmittercoil aligned at an angle to the borehole axis. Such devices have beenwell described in the past for dip determination. See, for example, U.S.Pat. No. 3,510,757 to Huston and U.S. Pat. No. 5,115,198 to Gianzero.

[0015] Co-pending U.S. patent application Ser. No. 09/474,049 (the '049application) filed on Dec. 28, 1999 and the contents of which are fullyincorporated herein by reference, disclosed a method of accounting forthe distribution of shale in a reservoir including laminated shaly sandsusing vertical and horizontal conductivities derived frommulti-component induction data. Data such as from a borehole resistivityimaging tool give measurements of the dip angle of the reservoir, andthe resistivity and thickness of the layers on a fine scale. Themeasurements made by the borehole resistivity imaging tool arecalibrated with the data from the induction logging tool that givesmeasurements having a lower resolution than the borehole resistivityimaging tool. A tensor petrophysical model determines the laminar shalevolume and laminar sand conductivity from vertical and horizontalconductivities derived from the log data. The volume of dispersed shaleand the total and effective porosities of the laminar sand fraction aredetermined using a Thomas-Stieber-Juhasz approach. Removal of laminarshale conductivity and porosity effects reduces the laminated shaly sandproblem to a single dispersed shaly sand model to which the Waxman-Smitsequation can be applied.

[0016] Co-pending U.S. patent application Ser. No. 09/539,053 (the '053application) filed on Mar. 30, 2000, having the same assignee as thepresent application, and the contents of which are fully incorporatedherein by reference, discloses a method of accounting for thedistribution of shale and water in a reservoir including laminated shalysands using vertical and horizontal conductivities derived frommulti-component induction data. Along with an induction logging tool,data may also be acquired using a borehole resistivity imaging tool. Thedata from the borehole resistivity imaging tool give measurements of thedip angle of the reservoir, and the resistivity and thickness of thelayers on a fine scale. The measurements made by the boreholeresistivity imaging tool are calibrated with the data from the inductionlogging tool that gives measurements having a lower resolution than theborehole resistivity imaging tool. The measurements made by the boreholeresistivity imaging tool can be used to give an estimate of V_(sh-LAM),the volume fraction of laminar shale. A tensor petrophysical modeldetermines the laminar shale volume and laminar sand conductivity fromvertical and horizontal conductivities derived from the log data. Thevolume of dispersed shale, the total and effective porosities of thelaminar sand fraction as well as the effects of clay-bound water in theformation are determined.

[0017] The method of the '053 application is not readily applicable toreservoirs in which the sands may be intrinsically anisotropic withoutmaking additional assumptions about the sand properties. Sands inturbidite deposits commonly comprise thin laminae having differentgrains size and/or sorting: the individual laminae may be isotropic buton a macroscopic scale relevant to logging applications, the laminationsexhibit transverse isotropy. In addition, a reservoir includingturbiditic sands exhibits an anisotropic permeability. Being able todetermine this anisotropic permeability is important from the standpointof reservoir development. This is an issue not addressed in the '053application and of considerable importance in development of hydrocarbonreservoirs.

SUMMARY OF THE INVENTION

[0018] In one aspect of the invention, a method of petrophysicalevaluation of a formation is disclosed wherein horizontal and verticalresistivities of the formation are inverted using a tensor petrophysicalmodel to give a first estimate of fractional volume of laminated shalein the formation. This first estimate of fractional volume of laminatedshale is comparted to a second estimate obtained from measurements ofdensity and/or neutron porosity of the formation using a volumetricmodel. If the second estimate of fractional shale volume is greater thanthe first estimate of fractional shale volume, the horizontal andvertical resistivities are inverted using a tensor petrophysical modelincluding the second estimate of fractional shale volume and obtaining avertical and horizontal resistivity of an anisotropic sand component ofthe formation. This vertical and horizontal resistivity of theanisotropic sand component is used in conjunction with at least oneadditional measurement selected from the group consisting of: of (i) NMRmeasurements of the formation, and, (ii) a bulk permeability of the sandcomponent to obtain properties a coarse and a fine grain portion of thesand component. The obtained properties of the coarse and fine grainportions of the sand include water saturations, and resistivities.

[0019] The properties of the coarse and fine grain portions of the sandare derived using an iterative solution process wherein a out of afamily of possible distributions of said properties, a selection is madethat matches the NMR measurement or the bulk permeability measurement.Relationships such as the Timur Coates equation may be used for thepurpose. The bulk permeability measurement may be obtained from aformation testing instrument, a pressure build up test, a pressuredrawdown test or from an NMR diffusion measurement.

[0020] Measurements of the horizontal and vertical resistivity may beobtained using a transverse induction logging tool, or from aconventional induction logging tool and a focused current resistivitytool.

BRIEF DESCRIPTION OF THE FIGURES

[0021]FIG. 1 (PRIOR ART) shows a resistivity imaging tool suspended in aborehole;

[0022]FIG. 2 (PRIOR ART) is a mechanical schematic view of the imagingtool of FIG. 1;

[0023]FIG. 2A (PRIOR ART) is a detail view of an electrode pad for thetool of FIGS. 1, 2;

[0024]FIG. 3 (PRIOR ART) is a pictorial view of a composite imaging logobtained by merging the resistivity image data shown in acoustic imagedata;

[0025]FIGS. 4A and 4B illustrate the principal steps of the process ofone embodiment of the invention.

[0026]FIG. 5A is a schematic illustration of the distribution of waterand hydrocarbons in a porous reservoir.

[0027]FIG. 5B shows the relationship between water saturation and thevolume of coarse grain sand in a porous rock.

[0028]FIG. 6A is a plot of resisitivity index as a function of watersaturation for a bimodal sand reservoir.

[0029]FIG. 6B shows the effect of water saturation on the resistivityanisotropy of a bimodal sand.

[0030]FIG. 7A shows possible solutions for the inversion of measuredresistivity of a bimodal sand reservoir.

[0031]FIG. 7B shows the dependency of spherical permeability of abimodal sand reservoir on the volume fraction of the coarse grainedcomponent.

DETAILED DESCRIPTION OF THE INVENTION

[0032] The present invention is best understood by referring to FIGS.1-7. FIG. 4 is a schematic flowchart of the major steps of the processused in the present invention. FIG. 1 shows a composite imaging tool 10suspended in a borehole 12, that penetrates earth formations such as 13,from a suitable cable 14 that passes over a sheave 16 mounted ondrilling rig 18. By industry standard, the cable 14 includes a stressmember and seven conductors for transmitting commands to the tool andfor receiving data back from the tool as well as power for the tool. Thetool 10 is raised and lowered by draw works 20. Electronic module 22, onthe surface 23, transmits the required operating commands downhole andin return, receives digital data back which may be recorded on anarchival storage medium of any desired type for concurrent or laterprocessing. A data processor 24, such as a suitable computer, may beprovided for performing data analysis in the field in real time or therecorded data may be sent to a processing center or both for postprocessing of the data.

[0033]FIG. 2 is a schematic external view of the unified boreholesidewall imager system. This may be used to provide the data that may beused in an optional embodiment of the invention. The tool 10 comprisingthe imager system includes four important components: 1) resistivityarrays 26; 2) electronics modules 28 and 38; 3) a mud cell 30; and 4) acircumferential acoustic televiewer 32. All of the components aremounted on a mandrel 34 in a conventional well-known manner. The outerdiameter of the assembly is about 5.4 inches and about five feet long.An orientation module 36 including a magnetometer and an inertialguidance system is mounted above the imaging assemblies 26 and 32. Theupper portion 38 of the tool 10 contains a telemetry module forsampling, digitizing and transmission of the data samples from thevarious components uphole to surface electronics 22 in a conventionalmanner. Preferably the acoustic data are digitized although in analternate arrangement, the data may be retained in analog form fortransmission to the surface where it is later digitized by surfaceelectronics 22.

[0034] Also shown in FIG. 2 are three resistivity arrays 26 (a fourtharray is hidden in this view). Referring to FIGS. 2 and 2A, each arrayincludes 32 electrodes or buttons identified as 39 that are mounted on apad such as 40 in four rows of eight electrodes each. Because of designconsiderations, the respective rows preferably are staggered as shown,to improve the spatial resolution. For reasons of clarity, less thaneight buttons are shown in FIG. 2A. For a 5.375″ diameter assembly, eachpad can be no more than about 4.0 inches wide. The pads are secured toextendable arms such as 42. Hydraulic or spring-loaded caliper-armactuators (not shown) of any well-known type extend the pads and theirelectrodes against the borehole sidewall for resistivity measurements.In addition, the extendable caliper arms 42 provide the actualmeasurement of the borehole diameter as is well known in the art. Usingtime-division multiplexing, the voltage drop and current flow ismeasured between a common electrode on the tool and the respectiveelectrodes on each array to furnish a measure of the resistivity of thesidewall (or its inverse, conductivity) as a function of azimuth.

[0035] The acoustic imager that forms the circumferential boreholeimaging system 32 provides 360° sampling of the sidewall acousticreflectivity data from which a continuous acoustic imaging log orsonogram can be constructed to provide a display of the imaged data.

[0036] The borehole resistivity imaging tool arrays necessarily allowsampling only across preselected angular segments of the boreholesidewall. From those data, a resistivity imaging log, consisting of datastrips, one strip per array, separated by gaps, can be constructed anddisplayed. The angular width of each data-scan strip is equal to 2 sin⁻¹{S/(2R)}, where S is the array width and R is the borehole radius. Thecommon data from the two imagers are merged together in a dataprocessing operation to provide a substantially seamless display asshown in FIG. 3. The merging incorporates equalizing the dynamic rangeof the resistivity measurements with respect to the acousticmeasurements. That balance is essential in order that the continuity ofa displayed textural feature is not distorted when scanning across aresistivity segment of the display, between adjacent acoustic segments.

[0037] The display in FIG. 3 incorporates measurements from directionalsensors to align the resistivity measurements with geographicalcoordinates (North, East, South, West), with the resistivity image being“unfolded” to provide a flat image of the cylindrical surface of theborehole. Those versed in the art would recognize that when a planeintersects a circular cylinder at an angle, the unrolled image of theplane would appears as a sinusoid. The display in FIG. 3 shows many suchsinusoids, some corresponding to bedding planes and others correspondingto fractures. The dip angle and the dip direction corresponding to thevarious sinusoids are determined in the present invention using knownmethods. When these data are combined with measurements from other logs,such as a gamma ray or a neutron log, discrete layers of differentlithologies may be identified. In particular, over a gross interval ofthe order of several meters or so, the fractional volume of laminatedshale present in a laminated reservoir may be determined.

[0038] With flat dips, the sinusoids have essentially zero amplitude. Inone aspect of the present invention, the resistivity measurements areaveraged circumferentially and vertically within each identified layerto give an average resistivity measurement for each layer identifiedabove. Once this is done, the subsurface may be characterized by anumber of plane layers, each of which has a constant resistivity. Withthe resolution of the button-electrode tool, these layers may range inthickness from a few millimeters to a few centimeters.

[0039] Those versed in the art would recognize that when the bedboundaries are dipping, then the currents into the electrodes,particularly those in the dip direction, on the pads may not be confinedto a single layer and hence not represent the resistivity of the layerat the borehole. In one aspect of the invention, the averaging describedabove is limited to electrodes in the strike direction: thesemeasurements would be more likely representative of the true formationresistivity at the depth of measurement.

[0040] The resistivity measurements obtained by the averaging processcorrespond to layers that are beyond the resolution of electromagneticinduction logging tools or propagation resistivity tools. Accordingly,the resistivity measurements obtained at this point are averaged to giveresistivities on a scale that would be measurable by an inductionlogging tool.

[0041] As would be known to those versed in the art, a finely laminatedsequence of layers having different resistivities exhibits a transverseisotropy on a larger scale where the wavelength of the electromagneticwave is much greater than the layer thickness. This condition is easilysatisfied even for propagation resistivity tools that, e.g., operate ata frequency of 2 MHz (with a wavelength λ≈6 meters); for inductionlogging tools that have frequencies of the order of 50 kHz to 200 kHz,the wavelengths are even longer. For such interrogating frequencies, thelayered medium is characterized by a horizontal resistivity R_(h)* and avertical resistivity R_(v)* given by: $\begin{matrix}{{R_{v}^{*} = {\frac{1}{W}{\sum\limits_{W_{t}}{R_{i}\Delta \quad h}}}}\text{and}} & (3) \\{\left( R_{h}^{*} \right)^{- 1} = {\frac{1}{W}{\sum\limits_{w_{t}}\frac{\Delta \quad h}{R_{i}}}}} & (4)\end{matrix}$

[0042] where W_(i) is a window used to average the resistivities, Δh isthe depth sampling interval of the electrodes, and R_(i) is the measuredresistivity for a given depth.

[0043] In this invention, the terms “horizontal” and “vertical” are tobe understood in terms of reference to the bedding planes and theanisotropy axes of the subsurface formations, i.e., “horizontal” refersto parallel to the bedding plane, and “vertical” refers to vertical tothe bedding plane. Where the beds of the formation are dipping, theanisotropy axis is taken to be the normal to the bedding plane. When theborehole is inclined to the bedding plane, data from the orientationmodule 36 in FIG. 1, may be used to correct the resistivity measurementsmade by the resistivity imaging tool to give measurements parallel toand perpendicular to the bedding planes.

[0044] Those versed in the art would recognize that the resistivitymeasurements made by the electrode-pad system described above may be inerror and, in particular, may need to have a scaling factor applied tothe data. When this data is acquired, it may be calibrated by relatingthe values given by equations (3) and (4) to data from an inductionlogging tool or a propagation resistivity tool.

[0045] Referring now to FIG. 4, one optional embodiment of the inventionstarts with data acquired by a borehole resistivity imaging tool such asis described in U.S. Pat. No. 5,502,686 issued to Dory et al., and thecontents of which are fully incorporated here by reference. It should benoted that the Dory patent is an example of a device that can be usedfor obtaining measurements borehole resistivity measurements: any othersuitable device could also be used. The process of the invention startswith an initial model 101 for the structure of the reservoir. Thisinitial model comprises a laminated shale fraction and a sand fraction.This initial model may be derived from the resistivity imaging tooldescribed above. A horizontal and vertical conductivity C_(sh-lam,h) andC_(sh-lam, v)) of the shale fraction is assumed or is measured 103; ifmeasurements are to be made within a borehole, this may be done by usinga Transverse Induction Logging Tool (TILT) on a thick section of shalein proximity to the reservoir. The resistivity of the “bulk” shale mayalso be obtained from core measurements.

[0046] An induction or wave propagation tool is used to makemeasurements of the vertical and horizontal resistivity of the earthformations. For example, U.S. Pat. No. 5,781,436 to Forgang et al, thecontents of which are fully incorporated here by reference, discloses amethod an apparatus for making measurements of horizontal and verticalresistivities of a transversely isotropic formation.

[0047] The method disclosed by Forgang et al comprises selectivelypassing an alternating current through transmitter coils inserted intothe wellbore. Each of the transmitter coils has a magnetic momentdirection different from the magnetic moment direction of the other onesof the transmitter coils. The alternating current includes a first and asecond frequency. The amplitude at the first frequency has apredetermined relationship to the amplitude at the second frequency. Therelationship corresponds to the first and the second frequencies. Themethod includes selectively receiving voltages induced in a receivercoil having a sensitive direction substantially parallel to the axis ofthe corresponding transmitter coil through which the alternating currentis passed. A difference in magnitudes between a component of thereceived voltage at the first frequency and a component of the voltageat the second frequency is measured, and conductivity is calculated fromthe difference in magnitudes of the components of the received voltageat the two frequencies. The Forgang patent is cited only by way ofexample of an induction device for obtaining horizontal and verticalresistivities of a formation and there are other teachings on obtainingthese properties of subterranean formation.

[0048] An example of a propagation resistivity tool for makingmeasurements of horizontal and vertical resistivities is described byRosthal (U.S. Pat. No. 5,329,448) discloses a method for determining thehorizontal and vertical conductivities from a propagation loggingdevice. The method assumes that θ, the angle between the borehole axisand the normal to the bedding plane, is known. Conductivity estimatesare obtained by two methods. The first method measures the attenuationof the amplitude of the received signal between two receivers andderives a first estimate of conductivity from this attenuation. Thesecond method measures the phase difference between the received signalsat two receivers and derives a second estimate of conductivity from thisphase shift. Two estimates are used to give the starting estimate of aconductivity model and based on this model, an attenuation and a phaseshift for the two receivers are calculated, An iterative scheme is thenused to update the initial conductivity model until a good match isobtained between the model output and the actual measured attenuationand phase shift.

[0049] As described in the '053 and '967 applications, measurementsR_(t,h) and R_(t,v) made by TILT or other suitable device are inverted111 to give an estimate of the laminar shale volume and the sandconductivity, assuming that the sand component is isotropic. In terms ofresistivity, $\begin{matrix}{R_{sd} = {\frac{1}{2} \cdot \left\{ {\left( {R_{sd}^{iso} + R_{{{sh} - l},m}} \right) + {\left( {R_{sd}^{iso} - R_{{{sh} - l},v}} \right) \cdot \sqrt{\left( {1 + {\Delta \quad R}} \right)}}} \right\}}} & (5)\end{matrix}$

[0050] where $\begin{matrix}{R_{sd}^{iso} = {{{R_{t,h} \cdot \frac{R_{t,v} - R_{{{sh} - l},v}}{R_{t,h} - R_{{{sh} - l},h}}}\quad \Delta \quad R} = {4 \cdot R_{sd}^{iso} \cdot \frac{R_{{sh},v} - R_{{{sh} - l},h}}{\left( {R_{sd}^{iso} - R_{{{sh} - l},v}} \right)^{2}}}}} & (6)\end{matrix}$

[0051] R_(sd) ^(iso) is the ‘isotropic’ sand resistivity. If the shaleis isotropic, (R_(sh,h)=R_(sh,v)), then this resistivity is identical tothe sand resisitivity. ΔR is the correction for anisotropic shale. ΔRbecomes zero for an isotropic shale (R_(sh,h)=R_(sh,v)).

[0052] The inversion also gives $\begin{matrix}{V_{{sh} - l} = {\frac{R_{sd} - R_{t,v}}{R_{sd} - R_{{{sh} - l},v}} = \frac{R_{sd}^{- 1} - R_{t,h}^{- 1}}{R_{sd}^{- 1} - R_{{{sh} - l},h}^{- 1}}}} & (7)\end{matrix}$

[0053] An independent estimate of the laminar shale volume V_(sh-l, TS)is obtained 107 from volumetric measurements using density or neutronlogs 105 and using a method such as the well-known Waxman-Smits orThomas-Stieber methods. Acoustic imaging logs may also be used to getthe volume fraction of laminar shale. Obtaining this independentestimate of laminar shale volume V_(shl, TS) would be known to thoseversed in the art and is not discussed further here.

[0054] Next, a check is made 113 to see if the V_(sh-l), from the TILTinversion agrees with the V_(sh-l, Ts) from neutron or density logs. Ifthe two estimates of laminar shale volume are consistent 115, then theassumption of an isotropic sand at 111 is valid and classical methodsbased on Archie or Waxman-Smits are used to determine water saturationof the sands. Alternatively, the Dual-Water method disclosed in the '053application are used to determine the water saturation in the sand.

[0055] If the answer at 113 is “No”, then a check is made to see ifV_(sh-l, TS) is greater than V_(sh-l). 117. If the answer is “Yes”, thenthis is an indication to change 119 the assumptions made at 103. Afterchanging the assumptions about the horizontal and vertical shaleconductivities, the process goes back to 101. If the vertical shaleconductivity is obtained from an actual measurement, then the assumedshale anisotropy factor is in error and a new value is chosen.Alternatively, the input parameters for the Thomas-Stieber calculationsmust be modified.

[0056] If the answer at 117 is “No”, then this is an indication that thesands component is anisotropic 121. In this case, the TILT resistivitydata are inverted 123 using the value of V_(sh-l, Ts) obtained at 107,e.g., using Thomas-Stieber and the method of the '049 application or themethod of the '053 application, to give a water saturation S_(w).

[0057] As a check on the determination of water saturation from theinversion of TILT data, NMR data are obtained 127 and from the NMR data,a determination of the bulk volume of irreducible water in the formationis made. Methods for determination of irreducible water saturationS_(w,irr) from NMR data are disclosed in U.S. Pat. Nos. 5,412,320 and5,557,200, the contents of which are fully incorporated herein byreference and not discussed further here. The bulk irreducible watercontent is given by S_(w,irr)φH, where φ is the porosity and H is thethickness, while the bulk water content from the TILT data is given byS_(w)φH. A check is made 129 to see if the former quantity is less thanthe latter quantity. If the test at 129 is negative, then it is anindication that there is a problem in the TILT model and the process isrestarted at 103. If the test at 129 is positive, then use is made ofhorizontal and vertical sand resistivities R_(sd,h) and R_(sd,v) in theTILT inversion 123 given by $\begin{matrix}{R_{{sd},h} = {\left( {1 - V_{{{sh} - l},{TS}}} \right)\left( {\frac{1}{R_{t,h}} - \frac{V_{{{sh} - l},{TS}}}{R_{{{sh} - l},h}}} \right)}} & (8) \\{R_{{sd},v} = \frac{R_{t,v} - {V_{{{sh} - l},{TS}} \cdot R_{{{sh} - l},v}}}{1 - V_{{{sh} - l},{TS}}}} & (9)\end{matrix}$

[0058] The sand anisotropy with resistivity values R_(sd,h) andR_(sd, v) is indicative of a laminated sand layer. These values ofR_(sd,h) and R_(sd, v) are inverted to give a layered model 131comprising isotropic sand layers and the laminated shale componentdetermined above. In order to perform this inversion, an estimate of thenumber and thicknesses of the sand layers is required. This may beobtained from a resistivity imaging tool as discussed in the '053 and'967 applications or it may be obtained using NMR data 127. From thedistribution of relaxation times T₁ and T₂ of NMR data, a distributionof volume fractions of individual sand components 133 may be obtainedusing known methods. Alternatively, core information or sedimentologicinformation about the reservoir may be used to give the volume fractionsof the sand components.

[0059] For the particular case of two components, eqns. (8) and (9) maybe inverted to give a unique solution for isotropic conductivities fortwo sand layers having the appropriate volume fractions. If the numberof sand layers in the laminated sand component is more than two, thenthere is no unique model of isotropic sand layers having an observedvertical and horizontal resistivity on a macroscopic scale. For the caseof more than two sand layers, additional information, such as somerelationship between the individual sand resistivities, is necessary toobtain the laminated sand component of the reservoir. The result of thisinversion 131 of a model of volume fractions (V_(sh-lam), V_(sd,1),V_(sd,2) . . . ) and resistivities (R_(sh-lam,v), R_(sh-lam,h),R_(t,sd,1), R_(t,sd,2) . . . ). For convenience, the discussionhereafter is limited to two sand layers though it is to be understoodthat additional layering of the laminated sand component is possible.

[0060] Using assumed values for the water saturated sand in horizontaland vertical direction R_(0,sd,h) and R_(0,sd,v) the water saturation ofthe individual sand layer S_(w,i) (i-th layer) are calculated separately135 using the layer resistivity R_(sd,i) obtained at 131. Depending onthe saturation equation (Archie-equation, Waxman-Smits-equation) thefollowing parameters are necessary as input: (i) Formation waterresistivity, (ii) porosity or formation factor of the layer, (iii)saturation exponent of the layer, and, (iv) Waxman-Smits-parameters incase of dispersed shale in the sand layer.

[0061] A direct method for saturation calculation for a bimodal sand isgiven in Schoen et al. As shown therein, a simple model is presented todescribe the influence of changing water content upon the electricalproperties for a thinly laminated bimodal Archie-type sand. The sandcomprises a coarse-grained component and a fine-grained component. Thecoarse sand fraction is characterized by low irreducible watersaturation and the fine fraction, by high irreducible water saturation.As shown in FIG. 5a, a single sand layer may be depicted by fourconstituents: the matrix 201, capillary bound water 203, movable water205 and hydrocarbon 207. The volume fraction of 203, 205 and 207 is theporosity of the sand. The change of water content only takes place inthe pore space occupied by the mobile fluid pore space (the combinationof 205 and 207). In this example, the pore space is occupied by immobilewater (capillary bound water) and movable fluids (movable water, oil,and gas). The complete pore space therefore is not available for thevariation of the water saturation, but only the mobile water fraction,1-S_(w,irr). Detailed information about the saturation behavior in theindividual layers could be derived from capillary pressure curves. Forthe simplified forward calculation this variation is expressed by aparameter defined as β and the total water saturation, assuming noclay-bound water, component can be written:

S _(w) =S _(w,irr)β·(1−S _(w,irr))=β+S_(w,irr)·(1−β)  (10)

[0062] The parameter β describes how the “free water pore space” isoccupied; for β=0,S_(w)=S_(w,irr) while for β=1, S_(w)=1.

[0063] For determining a variation of the total water content, oneembodiment of the present invention assumes that all sand fractions arecharacterized by the same value of for β but different S_(w,irr). Thus,the “free water pore space” is occupied in the same ratio for all sandfractions as it is described schematically in FIG. 5b. Shown in FIG. 5bis a plot of the water saturation (ordinate) as a function of thepercentage of coarse grained component of the sand (abscissa). Fivedifferent values of β are shown in the curves 221 a, 221 b . . . 221 e,the last of which corresponds to β=0 and having a value ofS_(w)=S_(w,irr).

[0064] For a two-component sand interval (e.g., coarse, subscript c andfine, subscript f) we have two different values for S_(w,irr)(S_(w,irr,c) and S_(w,irr,f)) and the vertical and horizontalresistivities are $\begin{matrix}{{R_{t,v} = {R_{w} \cdot \begin{bmatrix}{{V_{c} \cdot F_{c,v} \cdot {\quad\left\lbrack {\beta + {S_{w,{irr},c} \cdot \left( {1 - \beta} \right)}} \right\rbrack\quad}^{n}} +} \\{V_{f} \cdot F_{f,v} \cdot {\quad\left\lbrack {\beta + {S_{w,{irr},f} \cdot \left( {1 - \beta} \right)}} \right\rbrack\quad}^{n}}\end{bmatrix}}}\text{and}} & (11) \\{R_{t,h} = {R_{w} \cdot \begin{bmatrix}{\frac{V_{c}}{F_{c,h} \cdot \left\lbrack {\beta + {S_{w,{irr},c} \cdot \left( {1 - \beta} \right)}} \right\rbrack^{n}} +} \\\frac{V_{f}}{F_{f,h} \cdot \left\lbrack {\beta + {S_{w,{irr},f} \cdot \left( {1 - \beta} \right)}} \right\rbrack^{n}}\end{bmatrix}}} & (12)\end{matrix}$

[0065] where V_(c), V_(f) are the volume fractions of the coarse andfine sand, F_(c,v), F_(c,h), F_(f,v), F_(f,h) are the formation factorsfor coarse and fine sand related to vertical and horizontal currentdirection.

[0066] The mean saturation of the interval is $\begin{matrix}{S_{w}\quad \frac{{V_{c} \cdot \varphi_{c} \cdot \left\lbrack {\beta + {S_{w,{irr},c} \cdot \left( {1 - \beta} \right)}} \right\rbrack} + {V_{f} \cdot \varphi_{f} \cdot \left\lbrack {\beta + {S_{w,{irr},f} \cdot \left( {1 - \beta} \right)}} \right\rbrack}}{{V_{c} \cdot \varphi_{c}} + {V_{f} \cdot \varphi_{f}}}} & (13)\end{matrix}$

[0067] where φ_(c), φ_(f) are the porosities of the coarse and fine sandfraction. In a preferred embodiment of the invention, it is assumed thatthe two sand layers have the same intrinsic microscopic anisotropy ofthe formation factor. In most cases, this microscopic anisotropy of theindividual sand layers can be neglected when compared with themacroscopic anisotropy effect. Then the resistivity horizontal andvertical resistivity indices are

RI _(h) ={V _(c) ·[β+S _(w,irr,c)·(1−β)]+V _(f) ·[β+S_(w,irr,f)·(1−β)]^(n)}⁻¹  (14)

[0068] and $\begin{matrix}{{RI}_{v} = {\frac{V_{c}}{\left\lbrack {\beta + {S_{w,{irr},c} \cdot \left( {1 - \beta} \right)}} \right\rbrack^{n}} + \frac{V_{f}}{\left\lbrack {\beta + {S_{w,{irr},f} \cdot \left( {1 - \beta} \right)}} \right\rbrack^{n}}}} & (15)\end{matrix}$

[0069] The different saturations in the two sand fractions iselectrically described now by the two resistivity indices. With Eq. (13)the resistivity versus water saturation relationships can be calculated.FIG. 6a shows a logarithmic plot of the calculated resistivity index(ordinate) versus water saturation (abscissa). For each individual sandlayer, a saturation exponent index of n=equal to 2 was assumed. For theArchie relationship, the curve is a straight line 241 with a slope of 2.

[0070] All the curves in FIG. 6a correspond to an S_(w,irr,c)=0.1. Thecurves 243 a, 243 b are the vertical and horizontal resistivity indicesfor a value of S_(w,irr,f)=0.2; the curves 245 a, 245 b are the verticaland horizontal resistivity indices for a value of S_(w,irr,f)=0.3; whilethe curves 247 a, 247 b are the vertical and horizontal resistivityindices for a value of S_(w,irr,f)=0.5.

[0071] The anisotropy effect associated with the different partial watersaturations however results in the following:

[0072] (1) The saturation exponent relationship is a curve not astraight line and the saturation index exponent, n, of for the“composite” is dependent on water saturation.

[0073] (2) The vertical resistivity indices are much higher, and thehorizontal resistivity index indices are smaller when compared to valuesfor an Archie sand with n=2.

[0074] (3) The deviation of the resistivity index saturation exponentfrom n=2 increases with decreasing water saturation (increasinghydrocarbon saturation).

[0075] (4) For S_(w) equal to 1, both curves converge to the Archie n=2curve.

[0076] (5) All the saturation exponent variations are controlled by thecontrast in irreducible water saturation and volume fraction of thesands.

[0077] The ratios of resistivity anisotropy versus water saturation forthe case shown in FIG. 6a are shown in FIG. 6b for the same cases shownin FIG. 6a. As in FIG. 6a, S_(w,irr,c)=0.1. The curves 261, 263 and 265correspond to values of S_(w,irr,f) equal to 0.2, 0.3 and 0.5respectively. The abscissa is the mean water saturation while theordinate is the resistivity anisotropy ratio. FIG. 6b illustrates theremarkable influence of low water saturation (high hydrocarbonsaturation) on anisotropy. The maximum possible anisotropy ratio isdetermined by the maximum possible contrast of the two irreducible watersaturations. In this example, maximum anisotropy strongly trends to thehigher “mean” water saturation as a result of the high valueS_(w,irr,f).

[0078] Having reviewed the effect of water saturation on the anisotropyof a laminated sand, we now address the problem of inverting measuredvalues of horizontal and vertical resistivities for a laminated sand toobtain water saturations. The saturation determination problem forlaminated, bimodal sands can be described as follows:

[0079] (1) For the laminated macroscopic anisotropic sand, no constantsaturation exponent n can be defined.

[0080] (2) A formalistic application of Archie's equation with aconstant saturation exponent results in different saturation values forhorizontal and vertical measured resistivities, and a physicallyincorrect result.

[0081] In a preferred embodiment of the invention, a hydrocarbon-bearingbimodal sand, is modeled as comprising an alternating square stepprofile of a coarse (subscript c) and a fine fraction (subscript f).Other embodiments of the invention use other profiles, such as atriangular gradation of grain size between two limits. The calculationsfor such profiles would be readily obtainable for those versed in theart based upon discussions given here and in Schoen, Mollison & Georgi(1999) and are not discussed further.

[0082] The pore space of both sand layers has different watersaturation. The water saturation of the fine sand S_(w,f) is higher thanthe water saturation of the coarse sand S_(w,c). In particular,different grain sizes result in proportionately different pore sizes andcan be directly related to irreducible water saturation and capillarypressure. For both sands we assume that Archie's law is valid and noshale is present. The mean water saturation of the interval S_(w) is:

S _(w) =V _(c) ·S _(w,c) +V _(f) · _(w,f)  (16)

[0083] The horizontal and vertical resistivities of the compositesediment are determined as follows $\begin{matrix}{R_{t,h} = {R_{w} \cdot \left\lbrack {{\frac{V_{c}}{F_{h,c}} \cdot S_{w,c}^{n}} + {\frac{V_{f}}{F_{h,f}} \cdot S_{w,f}^{n}}} \right\rbrack^{- 1}}} & (17) \\{R_{t,v} = {R_{w} \cdot \left\lbrack {\frac{V_{c} \cdot F_{v,c}}{S_{w,c}^{n}} + \frac{V_{f} \cdot F_{v,f}}{S_{w,f}^{n}}} \right\rbrack}} & (18)\end{matrix}$

[0084] where F_(c,v), F_(c,h), F_(f,v), F_(f,h) are the formationfactors for the coarse and fine sands for the vertical and horizontalcurrent directions.

[0085] The following equations focus on the influence of the watersaturation upon the resistivity and anisotropy. For well-sorted sandsthe porosity is independent of grain size; thus, a reasonable assumptionis that the fine and coarse sand fraction porosities are similar.Further, it is attractive to assume that the formation factor is asimple single valued scalar. Therefore, in a first approximation, in thepreferred embodiment of the invention, we assume that within theinterval the formation factor is constant within the interval ofinterest. This assumption results in a simplification of the equations.

[0086] For the bimodal sand we derive three equations: horizontalresistivity index (Eq. 19), vertical resistivity index (Eq. 20), andvolumetric closure (Eq. 21): $\begin{matrix}{{RI}_{h} = {\frac{R_{t,h}}{R_{0,h}} = \left\lbrack {{V_{c} \cdot S_{w,c}^{n}} + {V_{f} \cdot S_{w,f}^{n}}} \right\rbrack^{- 1}}} & (19) \\{{RI}_{v} = {\frac{R_{t,v}}{R_{0,v}} = {\frac{V_{c}}{S_{w,c}^{n}} + \frac{V_{f}}{S_{w,f}^{n}}}}} & (20)\end{matrix}$

V _(c) +V _(f)=1  (21)

[0087] The inversion process results in two water saturation values,S_(w,c) and S_(w,f). This calculation requires the volume fraction ofone component (e.g., coarse component V_(c) or the fine component V_(f)as V_(f)+V_(c)=1). Possible sources of the sand grain-size distributionare whole sidewall core data or the addition of NMR log data.

[0088] Because n is not constant and Archie's law is not valid for thecomposite resistivity index, the following calculation is done to findone consistent solution for the water saturation values of the twolayers. We start with eqs. (19) and (20). From our a priori informationof the coarse component, S_(w,c,) ^(n) from eq. (19) is inserted intoeq. (20), resulting in the water saturation of the fine sand fraction:$\begin{matrix}{S_{w,f} = \begin{Bmatrix}{{\frac{1}{2}\left\lbrack \frac{{RI}_{h}^{- 1} + {{RI}_{v}^{- 1} \cdot \left( {1 - {2V_{c}}} \right)}}{1 - V_{c}} \right\rbrack} \pm} \\\sqrt{{\frac{1}{4}\left\lbrack \frac{{RI}_{h}^{- 1} + {{RI}_{v}^{- 1} \cdot \left( {1 - {2V_{c}}} \right)}}{1 - V_{c}} \right\rbrack}^{2} - \left\lbrack {{RI}_{v}{RI}_{h}} \right\rbrack^{- 1}}\end{Bmatrix}} & (22)\end{matrix}$

[0089] Note that only the positive root is physically realistic.

[0090] The water saturation of the coarse fraction can then bedetermined as $\begin{matrix}{S_{w,c} = {\left\{ {V_{c} \cdot \left\lbrack {{RI}_{v} - \frac{1 - V_{c}}{S_{w,f}^{n}}} \right\rbrack^{- 1}} \right\}^{\frac{1}{n}} = {\left( V_{c} \right)^{\frac{1}{n}} \cdot {\left\lbrack {{RI}_{v} - \frac{1 - V_{c}}{S_{w,f}^{n}}} \right\rbrack^{- \frac{1}{n}}.}}}} & (23)\end{matrix}$

[0091] Thus, both saturation values are obtained and the mean saturationis obtained from eq. (16).

[0092] Returning now to FIG. 4B, in an optional embodiment of theinvention, the results derived above are used for forward modeling ofthe properties of the reservoir rock 139 and a consistency check may bemade going back to 103. Still referring to FIG. 4B, an anisotropicpermeability calculation is made 141 for the reservoir with theproperties as derived above. This is accomplished as describedimmediately below.

[0093] The starting point for the permeability determination is theCoates-Timur equation $\begin{matrix}{k = {\left( \frac{\varphi}{C} \right)^{a} \cdot {\left( \frac{\varphi - {BVI}}{BVI} \right)^{b}.}}} & (24)\end{matrix}$

[0094] An alternate form of the equation is given by Kenyon ask=Cφ^(a)T^(b) and may be used. For the bimodal sand distribution derivedabove, for the two individual layers, the microscopic permeabilities are$\begin{matrix}{{k_{f} = {\left( \frac{\varphi_{f}}{C} \right)^{a}\left( \frac{\varphi_{f} - {BVI}_{f}}{{BVI}_{f}} \right)^{b}}}\text{and}} & (25) \\{k_{c} = {\left( \frac{\varphi_{c}}{C} \right)^{a} \cdot \left( \frac{\varphi_{c} - {BVI}_{c}}{{BVI}_{c}} \right)^{b}}} & (26)\end{matrix}$

[0095] The macroscopic permeabilities in the horizontal and verticaldirections are

k _(h) =V _(c) ·k _(c) +V _(f) ·k _(f)  (27)

and

k _(v) ={V _(c) ·k _(c) ⁻¹ +V _(f) ·k _(f) ⁻¹}⁻¹  (28)

[0096] Solution of eqs. (19)-(28) requires knowledge of the volumefractions of the coarse- and fine-grained components of the sand. Thismay be obtained from core analysis or from distribution of NMRrelaxation times.

[0097] In an alternate embodiment of the invention, eqs. (19)-(28) aresolved for a suite of values of V_(c) and V_(f) to give a family ofsolutions. Each of these has associated values of k_(h) and k_(v). Fromthese derived horizontal and vertical permeabilities, a globalpermeability is determined that averages over the individual layers anddirections. One such global measure of permeability is the sphericalpermeability given by $\begin{matrix}{k_{sph} = \left( {k_{h}^{2}k_{v}} \right)^{\frac{1}{3}}} & (29)\end{matrix}$

[0098] In a preferred embodiment of the invention, it is assumed thatthe permeability derived from NMR measurements is this sphericalpermeability. Alternatively, a permeability may be obtained using theformation testing instrument marketed by Baker Hughes under the markRCI™. Bulk permeability may also be obtained from reservoir pressurebuildup tests of pressure drawdown tests.

[0099] Having a measurement of the bulk permeability gives a uniquesolution to the inversion problem. In one embodiment of the invention,this solution is obtained using a nonlinear iterative algorithm. Such analgorithm would be known to those versed in the art and is not discussedfurther. Alternatively, the unique solution may be obtained by a tablelook up in a processor or by an equivalent graphical solution given inthe example below.

[0100] In order to test the method a data set was created by forwardcalculation. With the resulting data then the iterative inversionalgorithm was started.

[0101] Data for forward calculation: R_(W) = 0.1 Ohm m m = n = 2 V_(c) =0.4 V_(f) = 0.6 Φ_(c) = 0.34 Φ_(f) = 0.25 BVI_(c) = 0.05 BVI_(f) = 0.10using Coates equation the microscopic permeabilities are: k_(f) = 88 mdk_(c) = 4495 md

[0102] Result of forward calculation (macroscopic model data): R_(v) =22.0 Ohm m R_(h) = 14.3 Ohm m Φ = 0.286 BVI = 0.08 k_(h) = 1851 md k_(v)= 145 md k_(sph) = 791 md

[0103] Result of forward calculation (macroscopic model data): R_(v) =22.0 Ohm m R_(h) = 14.3 Ohm m Φ = 0.286 BVI = 0.08 k_(h) = 1851 md k_(v)= 145 md k_(sph) = 791 md

[0104]FIG. 7a shows the relationship between BVI_(c) and BVI_(f) for arange of assumptions of V c between 0.1 and 0.6, i.e., all the solutionsfit the measured resistivity values R_(v) and R_(h).

[0105] Turning now to FIG. 7b, three curves 311, 313 and 315 are shownof the spherical permeability (ordinate) as a function of Vc. The threecurves all have the same average porosity of 0.286 but the porosity inthe coarse fraction is 0.33 for 315, 0.34 for 313 and 0.35 for 311. Therange of values from 0.33 to 0.35 is a typical “noise” in thedetermination of porosity. A measured spherical porosity value isindicated by 321. It may be seen in FIG. 7b that a range of valuesbetween 325 and 327 for Vc are possible solutions to the inversionproblem. Table I gives the corresponding reservoir properties. TABLE IReservoir properties derived from combined analysis for three differentporosity assumptions Φ_(c) V_(c) BVI_(c) k_(c) (md) k_(h) (md) λ_(k)Φ_(f) V_(f) BVI_(f) k_(f) (md) k_(v) (md) 0.33 0.47 0.052 3318 1614 8.50.26 0.53 0.104 104 191 0.34 0.40 0.050 4493 1850 13 0.25 0.60 0.100 88145 0.35 0.37 0.046 6619 2039 19 0.24 0.63 0.095 76 109

[0106] It is worth noting that the determined permeability anisotropy(defined as a ratio of the horizontal to vertical permeability) rangesfrom 8.5 to 19. In comparison, the resistivity anisotropy, defined asthe ratio of the vertical to horizontal resistivity, is(22.0/14.3)˜1.54. Those versed in the art would recognize that acommonly used form of application of the Coates eqn. (26) is$\begin{matrix}{k = \left( {100 \cdot \varphi^{2} \cdot \frac{\varphi - {BVI}}{BVI}} \right)^{2}} & (30)\end{matrix}$

[0107] For BVI<<φ, the result is $\begin{matrix}{k = {10^{4} \cdot {\frac{\varphi^{6}}{{BVI}^{2}}.}}} & (31)\end{matrix}$

[0108] When combined with empirical relationships of Klein betweenpermeability and resistivity, the result is $\begin{matrix}{k_{v} = {{{10^{4} \cdot \frac{\varphi^{6}}{R_{W}} \cdot R_{h}}\quad k_{h}} = {10^{4} \cdot \frac{\varphi^{6}}{R_{w}} \cdot R_{v}}}} & (32)\end{matrix}$

[0109] This would imply that the resistivity and permeability anisotropyare equal, in contradiction to the results derived here. This apparentparadox results from the combination of macroscopic model equations forlaminated materials with microscopic empirical correlations betweenhydraulic connectivity and electrical resistivity.

[0110] While specific embodiments of the microresistivity tool andinduction logging tool have been discussed above, it is to be understoodthat the tools may be used either on a wireline or in an MWDenvironment. It is to be further understood that the anisotropymeasurements discussed above with reference to an induction logging toolmay also be obtained using a propagation resistivity tool. Specifically,in a preferred embodiment of the invention, a transverse inductionlogging tool has been described for obtaining measurements indicative ofhorizontal and vertical resistivities of formation. In an alternateembodiment of the invention, the horizontal resistivities may beobtained by a conventional induction logging tool with a coil axisparallel to the borehole axis while vertical resistivities may beobtained from measurements using a focused current logging tool. Suchfocused current logging tools would be known to those versed in the artand are not discussed further.

[0111] While the foregoing disclosure is directed to the preferredembodiments of the invention, various modifications will be apparent tothose skilled in the art. It is intended that all variations within thescope and spirit of the appended claims be embraced by the foregoingdisclosure.

What is claimed is:
 1. A method of petrophysical evaluation of aformation comprising: (a) using values of horizontal and verticalresistivities of the formation and deriving therefrom an estimate ofwater content thereof; (b) using NMR measurements of the formation andderiving therefrom an estimate of bulk irreducible water content of theformation; (c) comparing the estimate of water content with the estimateof bulk irreducible water content of the formation; and (d) obtaining aparameter of interest of the formation.
 2. The method of claim 1 whereinderiving said estimate of water content further comprises: (i) invertingsaid values of horizontal and vertical resistivities of the formationusing a tensor petrophysical model to give a first estimate offractional volume of laminated shale in the formation; (ii) obtainingmeasurements of density and/or neutron porosity of the formation andusing a volumetric model for deriving therefrom a second estimate offractional volume of laminated shale; and (iii) if said second estimateof fractional shale volume is greater than said first estimate offractional shale volume, inverting said horizontal and verticalresistivities using a tensor petrophysical model including said secondestimate of fractional shale volume and obtaining therefrom a bulk watercontent of the formation.
 3. The method of claim 1 further comprisingdetermining a vertical and horizontal resistivity of an anisotropic sandcomponent of the formation and determining therefrom and from at leastone additional measurement selected from the group consisting of: (i)NMR measurements of the formation, and, (ii) a bulk permeability of thesand component, a parameter of interest of a coarse and a fine grainportion of the sand component.
 4. The method of claim 1 furthercomprising using a transverse induction logging tool for obtaining saidvalues of horizontal and vertical resistivities of the formation.
 5. Themethod of claim 1 further comprising using an induction logging tool forobtaining said values of horizontal resistivities and a focused currentlogging tool for obtaining said values of vertical resistivities.
 6. Themethod of claim 1 wherein the tensor petrophysical model furthercomprises a laminated shale component and a sand component.
 7. Themethod of claim 1 wherein using said volumetric model further comprisesusing at least one of: (i) the Thomas-Stieber model, and, (ii) theWaxman-Smits model.
 8. The method of claim 3 wherein said parameter ofinterest is selected from the group consisting of: (A) a fractionalvolume of said coarse grain component, (B) a fractional volume of saidfine grain component, (C) a water saturation of said coarse graincomponent, (D) a water saturation of said fine grain component, (E) apermeability of said coarse grain component, and, (F) a permeability ofsaid fine grain component.
 9. The method of claim 3 wherein the at leastone additional measurement comprises an NMR measurement, and derivingthe parameter of interest further comprises deriving a distribution ofrelaxation times from said NMR measurements and obtaining therefrom adistribution of components of said anisotropic sand.
 10. The method ofclaim 3 wherein the at least one additional measurement comprises a bulkpermeability measurement of the anisotropic sand and deriving theparameter of interest further comprises: A. obtaining a family ofpossible distributions of volume fractions and bulk irreducible watercontent (BVI) for the coarse and fine sand components; B. determininghorizontal, vertical and bulk permeability values associated with saidfamily of possible distributions; and C. selecting from said family ofpossible distributions the one distribution that has a determined bulkpermeability substantially equal to the measured bulk permeability. 11.The method of claim 10 wherein said bulk permeability is obtained fromthe group consisting of (I) NMR diffusion measurements, (II) a formationtesting instrument, (III) a pressure buildup test, and, (IV) a pressuredrawdown test.
 12. The method of claim 10 wherein determining thehorizontal and vertical permeability values associated with said familyof distributions for the coarse and fine sand components furthercomprises using the Coates-Timur equation$k = {\left( \frac{\varphi}{C} \right)^{a} \cdot \left( \frac{\varphi - {BVI}}{BVI} \right)^{b}}$

where k is a permeability, φ is a porosity, BVI is the bound volumeirreducible, and a, b, and C are fitting parameters.
 13. The method ofclaim 10 wherein determining horizontal, vertical and bulk permeabilityvalues further comprises using a relationship of the form k=Cφ ^(a) T^(b) where k_(e) is a permeability, φ is a porosity and T is a NMRrelaxation time, and a, b, and C are fitting parameters.
 14. The methodof claim 13 wherein T is a longitudinal NMR relaxation time.
 15. Themethod of claim 2 wherein the tensor petrophysical model in (i)comprises at least one of (A) an isotropic sand component, and, (B) ananisotropic sand component.
 16. The method of claim 10 wherein thecoarse sand portion of the selected distribution is characterized by anirreducible water saturation less than an irreducible water saturationof the fine grain sand portion of the selected distribution.
 17. Themethod of claim 1 wherein deriving the parameter of interest furthercomprises specifying a formation factor for a constituent of theformation.
 18. The method of claim 10 wherein the determined bulkpermeability is a spherical permeability related to the horizontal andvertical permeability values by a relationship of the form$k_{sph} = {\left( {k_{h}^{2}k_{v}} \right)^{\frac{1}{3}}.}$


19. The method of claim 12 further comprising specifying the parametersa, b and C.
 20. The method of claim 13 further comprising specifying theparameters a, b and C.